English

The Secant Conjecture in the real Schubert calculus

Algebraic Geometry 2012-01-25 v3

Abstract

We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.

Keywords

Cite

@article{arxiv.1010.0665,
  title  = {The Secant Conjecture in the real Schubert calculus},
  author = {Luis Garcia-Puente and Nickolas Hein and Christopher J. Hillar and Abraham Martin del Campo and James Ruffo and Frank Sottile and Zach Teitler},
  journal= {arXiv preprint arXiv:1010.0665},
  year   = {2012}
}

Comments

19 pages

R2 v1 2026-06-21T16:23:33.474Z